General \(H\)-matrices and their Schur complements (Q2258094)

This paper presents an extensive fully theoretical study of properties of generalized \(H\)-matrices. It is known, that \(H\)-matrices can be divided into three disjoint sets -- the invertible class \(H^I\), the singular class \(H^S\) and the mixed class \(H^M\). The paper concentrates mostly on \(H^M\) and \(H^S\), however some results for the whole set \(H\) are also derived. Topics covered in the paper consist of conditions under which an \(H\)-matrix is (non)singular; convergence of the Jacobi iterative method for a linear system with a matrix being an \(H\)-matrix and properties of Schur complements with emphasize on matrices from the mixed class \(H^M\).